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李明翔, 泮斌峰. 行星着陆动力下降轨迹优化的中心差分凸化方法[J]. 深空探测学报(中英文), 2021, 8(2): 171-181. DOI: 10.15982/j.issn.2096-9287.2021.20200079
引用本文: 李明翔, 泮斌峰. 行星着陆动力下降轨迹优化的中心差分凸化方法[J]. 深空探测学报(中英文), 2021, 8(2): 171-181. DOI: 10.15982/j.issn.2096-9287.2021.20200079
LI Mingxiang, PAN Binfeng. Central Difference Convexification Method for Soft-Landing Trajectory Optimization in Planetary Powered Descending Phase[J]. Journal of Deep Space Exploration, 2021, 8(2): 171-181. DOI: 10.15982/j.issn.2096-9287.2021.20200079
Citation: LI Mingxiang, PAN Binfeng. Central Difference Convexification Method for Soft-Landing Trajectory Optimization in Planetary Powered Descending Phase[J]. Journal of Deep Space Exploration, 2021, 8(2): 171-181. DOI: 10.15982/j.issn.2096-9287.2021.20200079

行星着陆动力下降轨迹优化的中心差分凸化方法

Central Difference Convexification Method for Soft-Landing Trajectory Optimization in Planetary Powered Descending Phase

  • 摘要: 针对行星定点软着陆实时在线制导的任务需求,设计了基于序列凸优化的动力下降燃料最优轨迹求解算法。算法采用预标记的中心差分法线性化动力学方程,并提出将性能指标相对偏差作为收敛终止条件,能够快速生成燃料最优轨迹。此外,在分析最优轨迹簇剩余燃料和终端时间关系的基础上给出其拟合函数,作为最优终端时间的近似估算,以减少算法求解未知变量的维数。数值仿真结果表明,与对动力学方程先进行变量代换再线性化的传统凸化方法相比,该算法对初始猜想不敏感,收敛性好且终端误差较小。

     

    Abstract: Aiming at the mission of real-time online guidance for fixed-point soft landing on planet, the paper designs an algorithm based on sequential convex optimization that is designed to solve the fuel-optimal trajectory. The pre-labeled central difference algorithm is used to linearize the dynamics equations and the termination condition based on the deviation of index is proposed to judge whether it converges, which can generate a fuel-optimal trajectory quickly. Besides, a fitting function is given to approximately estimate the optimal terminal time by analyzing the relationship between the terminal time of optimal trajectories and their remaining fuel, which can reduce the amount of unknown variables. The simulation results of this algorithm show the weak sensitivity to initial guess, good convergence and small terminal error compared to the traditional convexification method of linearizing the dynamics equations whose variables are substituted at first.

     

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